Modified interpolation kernels for treating diffusion and remeshing in vortex methods

Daehyun Wee, Ahmed F. Ghoniem

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27 Scopus citations


A scheme treating diffusion and remeshing, simultaneously, in Lagrangian vortex methods is proposed. The vorticity redistribution method is adopted to derive appropriate interpolation kernels similar to those used for remeshing in inviscid methods. These new interpolation kernels incorporate diffusion as well as remeshing. During implementation, viscous splitting is employed. The flow field is updated in two fractional steps, where the vortex elements are first convected according to the local velocity, and then their vorticity is diffused and redistributed over a predefined mesh using the extended interpolation kernels. The error characteristics and stability properties of the interpolation kernels are investigated using Fourier analysis. Numerical examples are provided to demonstrate that the scheme can be successfully applied in complex problems, including cases of nonlinear diffusion.

Original languageEnglish
Pages (from-to)239-263
Number of pages25
JournalJournal of Computational Physics
Issue number1
StatePublished - 20 Mar 2006

Bibliographical note

Funding Information:
The research was supported by the Mathematical, Information, and Computational Sciences (MICS) program of the Office of Science in the US Department of Energy under the grant number DE-FG02-98ER25355. Computational support for large-scale scientific simulations was provided by the National Energy Research Scientific Computing Center (NERSC). The authors wish to thank the reviewers for their helpful comments, which contributed to improving the manuscript.


  • Computational particle methods
  • Diffusion
  • Numerical simulation
  • Redistribution
  • Vortex methods


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